The adjacent graph shows the extension (Δl) of a wire of length 1 m suspended from the top of a roof at one end and with a load W connected to the other end. If the cross-sectional area of the wire is 10⁻⁶ m², calculate the Young's modulus of the material of the wire:
Correct answer: A. A. 2 x 10^11 Pa
- A. A. 2 x 10^11 Pa
- B. B. 1 x 10^11 Pa
- C. C. 3 x 10^11 Pa
- D. D. 5 x 10^10 Pa
Explanation
To calculate Young's modulus (Y), use the formula Y =Stress/Strain. Here, Stress = Force (F) / Area (A) and Strain =Extension (Δl) / Original Length (λ). From the graph, you getthe values needed for these parameters:Stress = F/A = W / 10-6 m² and Strain = Δl / λ.Insert these into the Young's modulus formula:Y = (W / 10-6 )/ (Δl / λ) = (W × λ) / (Δl ×10-6).Using the data, calculate to get Y = 2 × 1011λ N/m2 Option A is correct because it accurately applies the formulaand concepts. Options B, C, and D are incorrect due tomiscalculations or misinterpretations of the data or formula.
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